This blog is about statistics, evolution, nutrition, lifestyle, and health issues. A combination of these issues. The focus is on quantitative research and how it can be applied in practice. But you may see other types of posts here (e.g., recipes, ideas, concepts, theories) from time to time.

Wednesday, January 20, 2010

Often in discussions about Paleolithic nutrition, and books on the subject, we see speculations about how long it would take for a population to adapt to a particular type of food. Many speculations are way off mark; some think that even 10,000 years are not enough for evolution to take place.

This post addresses the question: How long does it take for a food-related trait to evolve?

We need a bit a Genetics 101 first, discussed below. For more details see, e.g., Hartl & Clark, 2007; and one of my favorites: Maynard Smith, 1998. Full references are provided at the end of this post.

New gene-induced traits, including traits that affect nutrition, appear in populations through a deceptively simple process. A new genetic mutation appears in the population, usually in one single individual, and one of two things happens: (a) the genetic mutation disappears from the population; or (b) the genetic mutation spreads in the population. Evolution is a term that is generally used to refer to a gene-induced trait spreading in a population.

Traits can evolve via two main processes. One is genetic drift, where neutral traits evolve by chance. This process dominates in very small populations (e.g., 50 individuals). The other is selection, where fitness-enhancing traits evolve by increasing the reproductive success of the individuals that possess them. Fitness, in this context, is measured as the number of surviving offspring (or grand-offspring) of an individual.

Yes, traits can evolve by chance, and often do so in small populations.

Say a group of 20 human ancestors became isolated for some reason; e.g., traveled to an island and got stranded there. Let us assume that the group had the common sense of including at least a few women in it; ideally more than men, because women are really the reproductive bottleneck of any population.

In a new generation one individual develops a sweet tooth, which is a neutral mutation because the island has no supermarket. Or, what would be more likely, one of the 20 individuals already had that mutation prior to reaching the island. (Genetic variability is usually high among any group of unrelated individuals, so divergent neutral mutations are usually present.)

By chance alone, that new trait may spread to the whole (larger now) population in 80 generations, or around 1,600 years; assuming a new generation emerging every 20 years. That whole population then grows even further, and gets somewhat mixed up with other groups in a larger population (they find a way out of the island). The descendants of the original island population all have a sweet tooth. That leads to increased diabetes among them, compared with other groups. They find out that the problem is genetic, and wonder how evolution could have made them like that.

The panel below shows the formulas for the calculation of the amount of time it takes for a trait to evolve to fixation in a population. It is taken from a set of slides I used in a presentation (PowerPoint file here). To evolve to fixation means to spread to all individuals in the population. The results of some simulations are also shown. For example, a trait that provides a minute selective advantage of 1% in a population of 10,000 individuals will possibly evolve to fixation in 1,981 generations, or 39,614 years. Not the millions of years often mentioned in discussions about evolution.

I say “possibly” above because traits can also disappear from a population by chance, and often do so at the early stages of evolution, even if they increase the reproductive success of the individuals that possess them. For example, a new beneficial metabolic mutation appears, but its host fatally falls off a cliff by accident, contracts an unrelated disease and dies etc., before leaving any descendant.

How come the fossil record suggests that evolution usually takes millions of years? The reason is that it usually takes a long time for new fitness-enhancing traits to appear in a population. Most genetic mutations are either neutral or detrimental, in terms of reproductive success. It also takes time for the right circumstances to come into place for genetic drift to happen – e.g., massive extinctions, leaving a few surviving members. Once the right elements are in place, evolution can happen fast.

So, what is the implication for traits that affect nutrition? Or, more specifically, can a population that starts consuming a particular type of food evolve to become adapted to it in a short period of time?

The answer is yes. And that adaptation can take a very short amount of time to happen, relatively speaking.

Let us assume that all members of an isolated population start on a particular diet, which is not the optimal diet for them. The exception is one single lucky individual that has a special genetic mutation, and for whom the diet is either optimal or quasi-optimal. Let us also assume that the mutation leads the individual and his or her descendants to have, on average, twice as many surviving children as other unrelated individuals. That translates into a selective advantage (s) of 100%. Finally, let us conservatively assume that the population is relatively large, with 10,000 individuals.

In this case, the mutation will spread to the entire population in approximately 396 years.

Descendants of individuals in that population (e.g., descendants of the Yanomamö) may posses the trait, even after some fair mixing with descendants of other populations, because a trait that goes into fixation has a good chance of being associated with dominant alleles. (Alleles are the different variants of the same gene.)

This Excel spreadsheet (link to a .xls file) is for those who want to play a bit with numbers, using the formulas above, and perhaps speculate about what they could have inherited from their not so distant ancestors. Download the file, and open it with Excel or a compatible spreadsheet system. The formulas are already there; change only the cells highlighted in yellow.

11 comments:

Interesting post. I've run some large user-guided genetic algorithms in the past (in parallel, on around 1000 cpus). It's a real challenge to get the GA parameters tuned - ie population size, mutation rate, etc... The choice of representation and method of genetic crossover come into play as well, of course.

Anyway, the whole user-guided approach is further complicated because of user-fatigue. That is, how many individuals is a user willing to rank for fitness until exhaustion and frustration sets in? (it can be fascinating at first and then get very tedious!). The user's preference can be fickle and/or influenced by the ongoing simulation as well - that is, the fitness measure itself can be a moving target... The challenge, then, is to find an acceptable solution quickly before the user gets up and leaves.

In general, small populations lack diversity and tend to rapidly converge to local minima in the search space.

Conversely, large populations, while they have the most initial variation, might not converge towards the global minimum in an acceptable amount of time.

A simplification in the models I've run also assumes fixed population size per generation - as you point out above, populations grow in size over time...

Something I never got around to was to set up multiple sub-populations and occasionally migrate individuals from one population to another... And that's what I'm getting at: How would the the rate of migration of genetic material between sub-populations influence the estimate you provide above?

I think you know more about this topic than I do. It seems to me that migration would tip the scale toward genetic drift if it was emigration, and toward selection if it was immigration.

Below is a book where, I think, you can find an analytical and more elaborate answer to your question. You may know have read it already; the authors deal primarily with the evolution of social traits, taking migration and other factors into consideration. The reasoning applies to the evolution of any trait, in my opinion.

McElreath, R., & Boyd, R. (2007). Mathematical models of social evolution: A guide for the perplexed. Chicago, IL: The University of Chicago Press.

Thanks very much for the book recommendation! Just added it to my shopping cart.

You may find this paper of interest -http://www.pnas.org/content/early/2010/01/06/0909000107

I just came across it in a recent article in The Scientist titled "Ancient humans more diverse?".

http://www.the-scientist.com/blog/display/56279/

From the article:'Modern humans have an effective population size of about 10,000 -- a relatively low level of genetic diversity. ... This estimate of 10,000 has been regarded as stable for about 200,000 to 400,000, maybe "as far back as a million years", said population geneticist Chad Huff of the University of Utah (one of the paper authors)'

I think it is perfectly possible for a food-related trait to evolve in a much shorter time than often believed, but would that mean perfect adaptation in the sense of health and longevity?

These are very complex mechanisms, dependent on multiple genes and one mutation (say, lactose tolerance) would not necessarily mean that milk is now otimal food (there is casein with its opiate-like activity, perhaps different composition of fats, trace elements etc). Some mutations led to adaptation, but are clearly associated with bad health, e.g. haemoglobinopathies and G6PD deficiency (malaria), cystic fibrosis (plague) and many others. I would guess that many people can live on high carbohydrate diet without being obese and diabetic due to their ancestors' adaptation, but I hypothesise that they would not be in perfect health when you look at arteries, brain, skin etc. It would take many more thousands of years to fine tune the who machinery, to switch it to a new dietary paradigm than to make food tolerable.

But phenotype is not only genes and regulatory effects can compansate for genetic conservatism. Also, please to not ignore Lamarck completely. There may be a grain of truth in the inheritance of acquired traits, as claimed by neolamarckists based on modern molecular genetics (look at modern interpretation of Baldwin effect). But if Lamarck was right, we are not necesarily becoming better adapted, we might be getting more diseased "by nature" and pass the modified genes on. Just being devil's advocate.

Thanks for your kind words about this blog, which is mostly for the benefit of family and friends at the moment. Your blog is great!

I think you are correct. A fast evolution (e.g., 396 years) of a food-related trait would not necessarily increase longevity. For example, I suspect that the ancient Inuit evolved to be adapted to their heavy meat-and-fat diet, although longevity among them was not as high as in other traditional human groups (e.g., the Okinawans). Now it is much worse, due to their westernization.

As for Lamarck’s theory, I am intrigued by the work of McDougall (a bit old) and several others showing that indeed certain acquired traits appear to be inherited. But the counterarguments are also compelling. For example, McDougall showed that rats that learned how to solve a maze had offspring that also seemed to be better at solving the same maze. The counterargument is that those rats had genetic mutations that made them better at solving the maze in the first place, and passed those genes to their offspring – a Darwinian phenomenon.

Two interesting factoids that are related to this: (a) Darwin’s first edition of the “Origins” contained a clearly Lamarckian argument about what he called “use and disuse” or traits, which was removed from future editions; and (b) most non-behavioral traits (e.g., metabolic, morphological) seem to be preceded by related behavioral traits (e.g., preference for a type of food), even in organisms with a very simple nervous system - giving the impression of Lamarckian evolution when what is happening is purely Darwinian.

Finally, on your point about us becoming more diseased, I also think you are right. We as a species are most likely devolving, but very slowly and (in my view) due to Darwinian forces. In a population of billions, people develop genetic diseases all the time through stochastic mutation, many of whom survive to have children due to medical interventions, and pass the defective genes to the next generation. Selection pressures for health-promoting traits are very weak among modern humans.

It seems to me more likely that the epigenetics rather than the genetics are involved in short term adaption. The genes remain the same, but the expression is affected through at least several generations. You don't need to deal with mutations.. See Olov Bygren's study of families living in Overkalix. If girls were exposed to famine in utero or boys around the time of testicular development (germcell development for each sex), their "thrifty adaptation" would be passed on. If the subsequent generations were exposed to periods of plenty, they would get fat.

Ned Kock

About Me

I strongly believe that lifestyle, nutrition and exercise habits that are compatible with our evolutionary past are the key to optimal health. On the other hand, I do not believe that closely mimicking life in the Paleolithic is optimal for health, or even viable. I am a researcher, software developer, consultant, and college professor. Two of my main areas of research are nonlinear variance-based structural equation modeling, and evolutionary biology as it applies to the study of human-technology interaction. My degrees are in engineering (B.E.E.), computer science (M.S.), and business (Ph.D.). I am interested in the application of science, statistics, and technology to the understanding of human health and behavior. I blog about evolution, health, statistics, and technology. My personal web site contains links to my contact information and freely available articles related to the topics of my blogs: nedkock.com.

Copyright

The contents of this blog may be used with proper attribution. This blog makes limited use of copyrighted material (including tables and figures) for commentary, always with proper attribution and in ways that comply with fair use law.